


The Adventure of the Traversal Algorithm

by Irena_Lyre



Category: Sherlock (TV), Sherlock Holmes & Related Fandoms
Genre: F/M, Featuring ugly Venn diagrams, M/M, but there you go, go ask tumblr about tjlc, hell yeah S4 predictions, inspired by much tjlc meta, won’t be able to look at this thing again in the morning, writing(and drawing) under influence
Language: English
Status: Completed
Published: 2014-03-02
Updated: 2014-03-02
Packaged: 2018-01-14 05:50:28
Rating: Explicit
Warnings: Creator Chose Not To Use Archive Warnings
Chapters: 5
Words: 4,180
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/1255243
Author URL: https://archiveofourown.org/users/Irena_Lyre/pseuds/Irena_Lyre
Summary: <blockquote class="userstuff">
              <p>John Watson is but an ordinary man, but for a self-proclaimed genius and organisation freak, Sherlock Holmes is so not-smart in the classification of relationships, that he, too, employs the dumbest method: finding the right one by trying out every single of the wrong ones first. It is a costly process.</p><p>Surprisingly not an AU, but with much nerdism. S3 considered. Illustrations made with Excel.</p>
            </blockquote>





	1. 0.	The universal relationship plane^[citation needed], and the default state

The number of people on this planet is currently estimated to be 7 billion, which sounds like a lot. But then, the number of galaxies in this universe is currently estimated to be _at least_ 176 billion. I trust that you get the idea – it’s a big world, so overwhelming to our capacities, that our default state is nearer to total ignorance than anything else.

Naturally, it comes as no surprise, that the default state of the relationship between W. Sherlock S. Holmes and John H. Watson is, non-existent. They are utter strangers, as most people are to most people. The only binding factor in favour of their acquaintance is a common nationality, which represents a slim chance of bumping into each other on those busy isles. Since the British are generally careful not to bump into each other, they have lived into their thirties unaware of the existence of the other, and they are doing just fine.

Sherlock claims to be a scientist. Not that he demands out loud that people call him that, as it sounds like a silly title, but he prides himself in his methodical, analytical manners, in work and else. He constructs a logic tree for almost every puzzle, and trusts his own methods to lead to the most efficient path. The abhorrent last resort is to try everything exactly once; to repeat the same actions and expect a different outcome is the greatest folly, he would never do that.

John is not much of a scientist, but he is a doctor. A real, practical one who saves people, mind you, not the sort that dwells in unknown subjects and writes long paragraphs that don't get read. So practical that he went to war. He does not have Sherlock’s methods, but if the battlefield has ever taught him anything, he knows that when a place doesn’t feel right, the only reasonable course of action is to run away from it. Run and run, in circles if you must, until you’re in a spot that’s safe and happy. Requiring more instinct than brain, this is not the brightest of plans, but it works.

One day, 29th January 2010 to be exact, Sherlock and John are introduced, as acknowledged and confirmed by a handshake. Thus arises the necessity of pinning each other up on the relationship plane. For Sherlock, at least, because he likes classifying things, and people. John has not such a hobby, but for the handful of people in his life from three continents, he has his own fuzzy system of determining what to do with whom, for maximum enjoyment and minimum embarrassment, the least of hurtful things.

So, where does this new guy/acquaintance/flatmate belong?


	2. 1.	Local maximum #1

**Summary for the Chapter:**

> Time: immediately after TGG. Gratuitous smut.

The drama by the pool has ended differently than John expected, though for better or worse, he does not know. What he does know is that as they reach the top of the stairs into the flat, his blood is pumping faster than in the blazing heat of Afghanistan sands. John swallows, watching his flatmate toss down his jacket, the rise and fall of his chest all the more inviting under just a tight-fitting shirt.

Hot as ever, and as unattainable.

John has asked his question and gotten his answer on the very first night. Consequently, he has decided to be content, lest he should catch himself whining some _friend-zoning_ bullshit. At least the adrenaline is good, if nothing else. The same substance that sends the two of them springing across London roofs and down dark alleys is now twanging John’s veins. As Sherlock’s eyes turn to meet his, John senses a resonance in Sherlock’s look of uncertainty.

_You are married to your work._

_Well, just this once then, I don't mind. Do you?_

_Oh God, fuck me, it’d bloody better not be some sort of an experiment of yours._

_I assure you it’s not, now shut up._

John could not remember whether this exchange happened in proper words or between heated brushes of tongues. He does remember, distinctly, the ardent reception of his advances from Sherlock’s mouth that he did not deem possible. It is bolder than a typical first kiss, not that John would be assuming it to be Sherlock’s. It is still theirs, nonetheless. Fingers stumbling around annoyingly delicate shirt buttons, John’s mouth sucks and pulls at Sherlock’s exposed neck with hunger, until Sherlock pushes him away, making room for kneeling down to work on John’s trousers. John groans, holding back a breath as Sherlock yanks down his jeans, both hands on the waistband of John’s briefs. Sherlock pauses to look up to John, a ghost of a wink in his eyes.

If this is gratitude, then Sherlock Holmes has better manners than previously demonstrated. Also, John would not mind being strapped to a bomb and hugging a psychopath more often.

John’s half-erection springs free from the constrain, and the warmth of Sherlock’s palm immediately makes it more rigid. The ridiculous long fingers wrapped around his cock become pure madness, as the tentative strokes develop a rhythm. John leans back against the wall silently, his mouth hanging open in blissful agitation. An embarrassing whimper, soon to be followed by deep rumbles of utter joy, escapes his throat when Sherlock’s lips engulf the crown of his erection. Sherlock’s mouth slowly sucks in his length, where John’s own precum, mixed with saliva, slicks up the exquisite friction. The muffled noise from Sherlock’s throat sends John jolting, as he rakes his fingers through the artfully tousled dark curls.

“More,” John hisses a demand.

Sherlock hollows his cheeks in response, his lips reddened and glistening, his eyes heavy-lidded and drunk. For a second John could not decide which is better, the sight or the sensation. He slowly rocks his hip to get the most out of both, holding back the urge to fuck Sherlock’s mouth as hard as he would like. Sherlock grunts, pinning John’s hip with a hand, and _hums_. John shudders, forcing out a warning between his teeth and hard-bitten lower lip. Unrelenting, Sherlock’s other hand sneaks up to cup his balls, stroking them with the pad of his fingers, the playfulness eased by excessive saliva. John shatters, his body giving in to Sherlock’s mouth in a lasting groan, while Sherlock swallows greedily.

After a moment of wonder-struck breathlessness, John pulls his pants and jeans back up with calm, while Sherlock gets up from the floor, wincing for the soreness of legs. Without a word, John swings an arm around Sherlock’s waist, and tackles him to the ground.

“Come here,” John’s tongue swirls in Sherlock’s mouth for a taste of himself between broken words, “I’m not finished with you.”

“With all due respect, John,” Sherlock shoots back with an almost laugh, his hands crossing with John’s in unbuttoning, “it seems like you can’t get to it just yet.”

“No,” John moves down to the belt-buckle, “on my hands, smart git.”

“Oh, I’m going to need a bit more than that, Captain.” Sherlock smirks.

In response, John squeezes at his crotch still trapped in the fabrics. The scream elicited is satisfactory enough. Keeping with the rubbing over the bulge despite Sherlock’s cuss-words and pleas, John’s other hand wanders underneath Sherlock’s cotton tee-shirt to fondle a nipple. Sherlock arches excessively, eyes wide with lust and distress.

“Don’t forget that I am a doctor,” John leans over him, smiling treacherously, “and I do observe.”

Yes, John observes, perhaps a little more than appropriately, his insanely attractive flatmate whom he would shoot for and die for.

_And just this once, it’s all fine._

\---

John stares at the rug, momentarily forgetting his tea and toast in the kitchen, where Sherlock is already stationed, intensely concentrating on a suspicious small dish. The exact same spot where he has had Sherlock writhing in his hands begging last night, has now been vacuumed. Not a trace to be seen.

_Well, ask the man who could get rid of crime scenes but never vacuums._

Holding himself upright, John still feels a knot of unnamed defeat in his stomach. There could be no question about the quality of sex, so Sherlock must have decided against the attachment. All right. _More dates then._ And count on the brutally impartial comments therewith. With a huff, John strides up behind Sherlock to retrieve his breakfast. Something randomly flirtatious bubbles up in his head. He pops it, and walks out to the living room.

 _The water has been charted,_ and Sherlock steers away from it.

 

 


	3. 2.	Local maximum #2

**Summary for the Chapter:**

> Time: between TRF and TEH. Gratuitous nostalgia.

John takes off his date shoes as he enters the flat. His flat. He lives alone, presently, but he suspects the situation to change for the better soon enough, judging by how the evening has gone. He puts on the kettle in a no-longer-clustered kitchen, before dropping a lone teabag into one cup. To be fidgeting in someone’s presence, and to be grinning after good-nights have been exchanged, _yes,_ he remembers how it all feels like.

_Even if it’s not returned. Even if it's been almost two years._

_Now could be a new start._

“Hmm, you are not to spend the night - that’s discretion on her part - but stayed long enough after dinner. The nurse is not as boring as the others. See her again?”

John does not retort the voice that is not there. He huffs, flexing his fingers on his cup, and closes his eyes for a while.

\---

A few thousands of miles eastward, in a clinic whose modern interior contrasts so sharply against the natural landscape all around, a young nurse is watching over Sherlock Holmes. Negligence of food combined with fatigue will not serve one well in this climate, as arrogant white men sometimes forget. At any rate, this foreigner of peculiar features seems to be recovering faster than his lean form would suggest. Upon hearing a first sound from her patient, a smile reaches the eyes of the Mandarin girl, and she pulls off her gauze mask to call out to the doctor, who is busy talking to the monks in sporadic Tibetan.

“ _Jiong!_ ” she giggles, “I can’t believe the foreigner said jiong – he must be so embarrassed of himself for passing out.”

“Oh Xiao Liang, don’t be silly,” the doctor turns to her, frowning excessively, “the white man speaks no Mandarin. Don't you know that John is the name of one of the four gospels? Maybe this patient is a devout Christian. A missionary, even.” Long years on the Plateau have seasoned the doctor, as to suggest a _divine_ association to a male name, before a _romantic_ one.

“Then what in the world is he doing in a Buddhist monastery? Preach?” the girl shrugs, revealing more of the pale green military shirt underneath the white robe.

“The word is that he cracked a drug gang, without being invited by our police, which is an offence in itself.” The older man runs a hand over the lines on his forehead. “But who knows the schemes of these westerners? We are just performing humanitarian duties by saving them, so they could carry on prying our vast and unguarded territory. What a shame.”

Despite the distinguishable tone of distain, the string of blurry alien words actually serve to pacify Sherlock’s swaying consciousness. Even in this strange land, Sherlock Holmes gets an equally grumpy army doctor to take care of him. What are the odds? To be away, away from John, is supposed to be a part of the plan, yet he regrets what Mycroft did not foresee or chose to overlook. In the howling winds of the world’s third pole he thinks of the cluster of faded blanket on the couch of 221B. Of course John would toss it his way, while nagging at or even begging him to at least take some tea with sugar. _Never thought he’d miss the nagging._ The ringing headache sets in again, albeit much less in magnitude than before, and Sherlock softly calls out John’s name a few more times. John. _John._ In a safe sphere of incomprehension, the simple syllable is a lucky charm to ward off evil, and a compass to what was and what could be. An anchor, a golden ray of hope.

Let them mistake it for whatever they care to think of. John is kept from the rest of the world, and for that, Sherlock is glad.

**Notes for the Chapter:**

> Footnote: Jiong, which sounds close enough to John, is a Mandarin word which originally means brilliance and brightness, but has recently taken on the meaning of extreme awkwardness or embarrassment, due to the character's resemblance to a low-hanging face. *end of random helpful fact*


	4. 3.	A spatial discontinuity

**Summary for the Chapter:**

> Time: Post-HLV. Wild porn(not really).

**Notes for the Chapter:**

> Borderline infidelity in this bit. If don't like, please don't read. Many thanks!

In a way, Sherlock has given up. Not that he would be blaming John for what has come to be; in fact, quite the opposite. Whatever did NOT happen on stag night has been shoved into the dungeon of his Mind Palace, not to be released for eternity. It is a scientifically established fact that the attractiveness of _anyone_ would increase in the eyes of the beer-holder. Case closed.

Right now, Sherlock has just finished cooing the baby girl, and handed her back to Mrs. Watson, the woman with whom he has made peace after she _shot_ him. John is stuffing yet more supplies into a rucksack, making it as stretched as his jumper - he has further gained four pounds, as manifest by the lump of his belly. _Like an American family guy straight from crap channels._ Sherlock hides a grin. It’s sometimes comical, verging on ridiculous, to see John so _normal_. _As he wishes_. Does this drag Sherlock towards the course of normalcy as well? Visiting a friend – friends, hugging their baby, etc. An amusing, yet faintly frightful prospect.

“Have a good time,” John kisses his woman, then his child.

“John, you behave.” Mary squeezes him on the elbow, and calls out behind him. “Sherlock, watch him for me, will ya?”

“Sure,” Sherlock gives her a somewhat stiff thumb-up, a mannerism he’s just picking up. John grimaces abundantly.

As the car pulls out of the driveway, John’s shoulders relax visibly. He strides up to the balcony and huffs deeply. He could well be reaching for a cigarette, if he smokes. Facing the afternoon sun, he squirms at Sherlock, who is still waving at the vanishing vehicle.

“You like her more than I do, don’t you.” It is a mere observation.

Turning to John, Sherlock squirms likewise. “Little Miss Watson is perfectly likeable, unlike her grumpy papa.” He snorts.

John sighs, with a wry smile. “No, not my daughter. That I love more than anyone ever will. I was talking about my _wife_.”

Sherlock stills for a moment, and says, “Mrs. Watson is perfectly likeable as well.”

“Oh yes, and perfectly smart.” John closes in half a step. “Come inside with me. Why do you think she invited you over on the day of her road trip, genius?”

Sherlock’s heart races. They have not really talked about any of these since the turnaround of the plane – all the proof in the world that the refrain from outbursts of emotions is worthy. He swallows.

_We tried everything, every combination of things, we did. And here we are, stuck. There’s nowhere else to go, John, nowhere._

John raises his chin. _Oh, no, not everything. When there’s nowhere to run, try jumping across, if it makes you happy._ He lowers his head a little in guilt.

Sherlock stares, a shadow of sadness creeping up in his eyes. _I already forgot what happy feels like_.

_Then get it. I will gladly do the honour of reminding._

Sherlock growls. _I am not your fix-it._

John gestures for calm. _No, absolutely not. I am not asking you to be. Just… take what you need, no worries. We’ve done this before, remember?_

_Yes, I remember some parts of_ that _._ Sherlock spits. _No, we have not done_ this _before. I do not_ need _the_ husband _of any other._

John is unrelenting. _Yes, you have, you said you were married to your work. And_ just this once _._

Sherlock chortles. _John Watson, listen to yourself. What exactly is it you are justifying?_

“You.” John answers truthfully, pulling Sherlock down by both lapels. Sherlock, wholly flustered, does not resist the fall to the creamy carpet smelling of detergent. _So domestic. Too well-kept. Suffocating._

_Well, trying out the other extreme wouldn’t hurt anything._

_Since there is nothing left to hurt anyway._

John’s hands are everywhere on Sherlock’s stretched body, John’s voice low and hot against his earlobe. “The floor has a special appeal. Easier to clean up, I guess? Not a trace, you would know.”

John’s latent grudge from over a few years ago goes fortunately unregistered by Sherlock, who manages to hiss through heated breaths. “Mary knows… anyway.”

“Yes, she does, now shut up.” John darts his tongue into Sherlock’s parted lips in desperation, taking in as much long-forsaken sweetness as he can. The heat between their partially stripped upper bodies makes John shiver. He longs to make Sherlock melt underneath him, yet this is supposed to be cold sex, a fuzz-free distraction, a basic want, colder than their last, first, only time, to be simply dropped where it finishes, like good bullet shells –

_Speaking of bullets._

As John presses his palm on Sherlock’s bare chest, a circle of darkened pink tissues more than stings. John sobers up instantly. He glances at his own left shoulder. While Sherlock’s distortion, smaller in dimension, does not look as bad, it must have hurt more.

Sherlock freezes in trepidation. To feel the bulge in John’s groin flacciding against his own might have been an object of merry-making in another setting, but right here, he is petrified. John’s face, firmly pressed against his chest, is hidden from view. The helpless sniffles and streams of warmness on Sherlock’s skin give him away. Biting the inside of his own lips, Sherlock lightly pats John’s bare shoulders in a timid manner like they do on TV, and whispers softly, “John, I’m sorry.”

_This is a dead-end._

John’s head snaps up. The glare in his tearful blue eyes is scary to Sherlock more than anything else. “Don't you ever fucking say you’re sorry about _this_ , Sherlock. _You_ are not sorry.” John steadies his breath with great effort. “I – ah, I screwed up.”

Sherlock blinks, his mind scanning for something to say. “Well, it – surely it’s not the first time that has happened.” John chokes out a laugh. “We both screwed up. But we are grown men, John, we have lived our lives before we met, and we dealt with things, terrible things, just fine. Can we still do that now?”

John’s face softens. With a faint smile, he cups Sherlock’s jaw line in his hands to press a chaste kiss to his lips, before pulling him up from the ridiculous carpet. “Absolutely. Now put your cloths on and go home.” Sherlock grins faintly, his lips stiff and tight. “I will come to you.” John adds.

“To me?” Sherlock raises an eyebrow.

“Don’t get your hopes up, smart-arse, it won’t be tomorrow, this week, or even this month.” John picks up his own shirts from the floor to put them back on. He looks like he’d grab Sherlock once more; instead, he says, quietly, “But when I do come home, I will stay home.”

_Why, yes, after trying everywhere else._

__

**Notes for the Chapter:**

> Phew! Only one bit left! Anyone who has made good sense out of the crazy Venn diagrams - I applaude you, and would like to give you a cookie, seriously.


	5. 4.	The global optimum

**Summary for the Chapter:**

> The worst and the best defence for a solution is, that nothing else works.

**Notes for the Chapter:**

> Implied divorce in this bit. If don't like, please don't read. Thank you!

Janine takes a sip of her hot chocolate and smiles. Not at the sub-par beverage of Speedy’s, but at her haughty companion across the table. Well, ex-fiancé, in a way. Those once considered worthy of employment by the mighty C.A.M. are not easily besotted, and the girl with an easy laugh never held much grudge against her share of time in the flat overhead or its occupant, who reluctantly agreed to come down despite the obvious lack of any real business on Janine’s part. _Oh, he is lonely._

“Any word from your boyfrand?” she teases.

“I don’t have a _boyfriend_.” Sherlock sounds slightly defensive. Mrs. Hudson, Irene, now Janine, all these women in his life keeps saying silly things. _Insufferable_.

“Well, I guess you’re way past that.” Janine puts down her mug, her voice stained by pity and a tinge of triumph. “But I’m afraid you’re not getting to call him _fiancé_ anytime soon, Sherlock.”

Sherlock needs say nothing to that. Indeed, he has not heard from John. He would _want_ to have, but not _need_ to. John is a grown man, if he decides on something, he will find a way to it, Sherlock is counting on that. He grimaces at the taste of plain tap water, but swallows it anyway.

“Enough about your life, that’s all you’ve got going on anyway. Now mine.” Janine is amused by the absence of denial, and goes on. “Long story short, I’m moving. To southern France.”

Sherlock nods. “Good. Give him my regards, if you’re compelled.”

“Oh, don’t worry, he’s read the papers. That’s how we started talking, actually, so I thought I should say thanks?” Janine giggles a bit, half at the flashbacks. She reaches for his hand to squeeze it gently. “Never thought I’d be saying this, Sherlock Holmes, but you are a good man, and I hope it all works out for you.” She stands up, swinging on her coat. “Now do I get a good-bye kiss?”

Sherlock scoffs. It is a pattern now, how these women would swoon in his presence at first, but then end up cooing him like a big gooey baby. Even Molly does it now. Somehow he misses the slaps in his face. “No, Janine, goodbye. Bon voyage!”

Janine purses her lips. “Oh, bad Sherl, I was going to talk about the cottage that I didn't sell.”

“ _What?_ ”

“Well, I can’t find anyone to get rid of the beehive humanely.”

\---

John is hauling his luggage back into 221B, considerably more burdened than when he moved out. Combining the bedrooms would be a sensible thing to do, making room for a child. Not that they are there _yet_. From now on John would like to take things slow. Not that moving straight back in _with a child_ is any sign of slowness. He eyes the overflowing volumes on childcare and child psychology around the flat, and feels a familiar knot in his stomach.

Any way, he is back.

“We do have other options if you prefer a more… pastoral setting.” Sherlock offers. John notices his fidgeting, and a warm smile reaches the creases around his eyes. He feels older now. But in a good, daddy-like way. So is his _flatmate_ in front of him. This is not the same man from 2010, or 2012, or even 2014. They have both come such a long way, of ridiculous twists and turns and circles.

_Brute-force cracking of anything is so consuming._

“Day-care is good enough for now, we’ll see. To leave London would be an entirely new project.”

Sherlock hums an agreement, and says nothing more. Rife with his own apprehension, John stumbles for something to ease Sherlock’s mind. “May I court you properly now?” he tries, hardly looking up to his would-be boyfriend.

“Oh, come on.” Sherlock’s lips are upon his, and John kisses him back slowly and deeply. It is not their first kiss in any measure, yet it is. John’s teeth nibbles here and there, and he feels absolutely entitled to every little noise. “Sit,” John murmurs, guiding Sherlock backwards into Sherlock’s own chair. He straddles Sherlock’s lap and pauses, waiting for Sherlock to remember a faintly similar setting.

“Oh,” Sherlock breathes, in realisation.

“This is where we have been, and where we are at, after _everywhere_ else.” John says somewhat solemnly, his fingers stroking down Sherlock’s face.

“Well, not _everywhere_.” Sherlock leans back to John’s dismal, assuming a thinking pose. “Out of theoretical probability, John, has it ever occurred to you that our relationship could have been non-positive? As in, I don’t even know you. Or you could be my enemy of various degrees.”

“Well, sometimes I do hate you.” John gazes downwards, “For _existing_.”

“And I have tried being dead.” Sherlock says quietly.

John pauses for a moment, some of the long-forgotten hurt resurfacing. Yes, he said sorry a handful of times, but John still needs more. “And it works for you?” he grits his teeth.

“No, it doesn’t, it was terrible.” Now that’s a first. Sherlock buries his face in John’s chest, and John lets him. “I missed you, John.”

John stills to feel the warmth of breaths against his skin through his shirt, and holds Sherlock in closer, years of unresolved ponderings released in one exhale. “I missed you too, Sherlock, I missed you too.”

\---

As the natural course of things, W. Sherlock S. Holmes and John H. Watson, who have subsequently altered their family names which is beyond the scope of discussion here, do become arch-enemies in the end, as evident in their reoccurring daily struggles to cohabit. Here described is the process through which they have placed each other more accurately than the rest of the 7 billion people on this planet, though their approach has proven them both to be below average on the intelligence front, Q.E.D. The moral of the story, my dear readers, is that even the brute-force traversal algorithm could be justified, if the object to be placed is deemed important enough.

Problem?

-END-

**Notes for the Chapter:**

> 1\. Nothing against Speedy's (is it even a real operating shop? Or like, just a prop), any words of mine regarding their product is for the story only.
> 
> 2\. I totally understand how people can get upset about divorce - I am not a big fan of it either, but in any circumstance I consider it a better way to get rid of a spouse than premature DEATH.
> 
> 3\. This story is written on a whim and somewhat experimental, and I am grateful to all of you who bore with it. But did anyone get the Venn diagrams? Can you even see them? They were uploaded on Tumblr, and sometimes may not properly show up. The graphics crave improvement, and I could have labeled them better, apologies. Hopefully they've been helpful, or fun, or at least not annoying. *nerd intensifies*

**Author's Note:**

> For the longest time I pretended that S3 does not exist, but now after much tjlc meta I've decided to have fun with it.  
> To those who have endured my writing thus far, thank you.


End file.
